(6/(x-5))+(2/(x+5))=84/(x^2-25)

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Solution for (6/(x-5))+(2/(x+5))=84/(x^2-25) equation: 


D( x )

x-5 = 0

x+5 = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x^2-25 = 0

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in (-oo:-5) U (-5:5) U (5:+oo)

6/(x-5)+2/(x+5) = 84/(x^2-25) // - 84/(x^2-25)

6/(x-5)+2/(x+5)-(84/(x^2-25)) = 0

6/(x-5)+2/(x+5)-84*(x^2-25)^-1 = 0

6/(x-5)+2/(x+5)-84/(x^2-25) = 0

(6*(x+5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(2*(x-5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(-84*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0

6*(x+5)*(x^2-25)+2*(x-5)*(x^2-25)-84*(x-5)*(x+5) = 0

8*x^3+20*x^2-84*x^2-200*x-500+2100 = 0

8*x^3-64*x^2-200*x+1600 = 0

8*x^3-64*x^2-200*x+1600 = 0

8*(x^3-8*x^2-25*x+200) = 0

x^3-8*x^2-25*x+200 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 20, -20, 25, -25, 40, -40, 50, -50, 100, -100, 200, -200 }

1

x = 1

x^3-8*x^2-25*x+200 = 168

1

-1

x = -1

x^3-8*x^2-25*x+200 = 216

-1

2

x = 2

x^3-8*x^2-25*x+200 = 126

2

-2

x = -2

x^3-8*x^2-25*x+200 = 210

-2

4

x = 4

x^3-8*x^2-25*x+200 = 36

4

-4

x = -4

x^3-8*x^2-25*x+200 = 108

-4

5

x = 5

x^3-8*x^2-25*x+200 = 0

5

x-5

x^2-3*x-40

x^3-8*x^2-25*x+200

x-5

5*x^2-x^3

200-3*x^2-25*x

3*x^2-15*x

200-40*x

40*x-200

0

x^2-3*x-40 = 0

DELTA = (-3)^2-(-40*1*4)

DELTA = 169

DELTA > 0

x = (169^(1/2)+3)/(1*2) or x = (3-169^(1/2))/(1*2)

x = 8 or x = -5

x in { -5, 8, 5} 

8*(x+5)*(x-8)*(x-5) = 0

(8*(x+5)*(x-8)*(x-5))/((x-5)*(x+5)*(x^2-25)) = 0

(8*(x+5)*(x-8)*(x-5))/((x-5)*(x+5)*(x^2-25)) = 0 // * (x-5)*(x+5)*(x^2-25)

8*(x+5)*(x-8)*(x-5) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-5 )

x-5 = 0 // + 5

x = 5

( x-8 )

x-8 = 0 // + 8

x = 8

x in { -5} 

x in { 5} 

x = 8

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